THE SOUTH AFRICAN
MATHEMATICS OLYMPIAD
organised by the SOUTH AFRICAN ACADEMY OF SCIENCE AND ARTS in collaboration with OLD MUTUAL, AMESA and SAMS
SPONSORED BY OLD MUTUAL
FIRST ROUND 2000
JUNIOR SECTION: GRADES 8 AND 9
12 APRIL 2000
TIME: 60 MINUTES
NUMBER OF QUESTIONS: 20
Instructions:
1. Do not open this booklet until told to do so by the invigilator.
2. This is a multiple choice question paper. Each question is followed by answers marked A, B, C, D and E. Only one of these is correct.
3. Scoring rules:
Each correct answer is worth 5 marks. There is no penalty for an incorrect answer or an unanswered question.
4. You must use an HB pencil.
Rough paper, ruler and rubber are permitted.
Calculators and geometry instruments are not permitted.
5. Diagrams are not necessarily drawn to scale. 6. Indicate your answers on the sheet provided.
7. When the invigilator gives the signal, start the problems.
You will have 60 minutes working time for the question paper.
PRACTICE EXAMPLES
1. 23+ − =6 4
(A) 6 (B) 23 (C) 25 (D) 29 (E) 33
2. 1
5 2 3
1 2
+ × equals
(A) 1 B) C) D) E) 9
15
3 11
21 50
8 15
4 5
( ( ( (
1 identical to Box B will fill Box A exactly?
(A) B)
3. What number should be in the square in the following pattern of numbers?
1
8. The number of times the hour hand and the minute hand of a clock form a right angle with each other between 06:00 and 12:00 on the same day is
9. The average (arithmetic mean) of three numbers is 18. If one of the numbers is replaced by the number 38, then the average of the three numbers is 23. The original number that was replaced is
(A)38 (B)23 (C)15 (D)18 (E)33
10. If the following pattern continues and the numbers in the 100th row are added, the answer will be it takes to fill the remainder of the container, at the same rate, is
A the same pace. One ant walks around a 3 cm by 3 cm square whilst the other walks around a 6 cm by 3 cm rectangle. What is the minimum distance, in centimetres, any one must cover before they meet again?
(A)18 (B)72 (C)216 (D)36 (E)108
13. The letters A to I represent numbers. The numbers are added vertically and horizontally to give the numbers in the last row (17; P; Q) coloured green, one red, one blue and one yellow. The number of different ways they can be stacked one upon the other is
(A) B) C)
n numbers
1 + 3 + 5 + 7 + 9 + … = 2304
x
D
A E B
F C
16. The size of angle x, in degrees, in the regular octagon is
(A) B) C)
D) E)
90 67 5 45
60 75
( , (
( (
17. ABCD is a rectangle. E and F are midpoints of AB and CB respectively. If the area of the shaded ∆AEF is 7 cm2, then the area of rectangle
ABCD, in square centimetres, is
(A) B) C)
D) E)
28 49 42
35 56
( (
( (
18. Three rulers and one pencil cost the same as two erasers. One ruler, two pencils and three erasers cost R25. If the price of each item is a whole number of Rands, then the price of an eraser is
(A) R B) R C) R D) R
E) impossible to find
2 ( 3 ( 4 ( 5
(
19. Increasing 800 – 10x by 10% gives 600 – 6x. The value of x equals
(A)45 (B)40 (C)56 (D)80 (E)50
20. The sum of the first n odd natural numbers is 2304.
The value of n is
(A)123 (B)50 (C)46 (D)48 (E)69
ANSWER POSITIONS: JUNIOR FIRST ROUND 2000
PRACTICE EXAMPLES
POSITION
1 C
2 D
NUMBER POSITION
1 B 2 A 3 B 4 D 5 E 6 E 7 A 8 B 9 B 10 A 11 C 12 D 13 A 14 D 15 B 16 C 17 E 18 D 19 C 20 D
DISTRIBUTION
A 4
